A. Geyer and D.E. Pelinovsky

Spectral stability of periodic waves in the generalized reduced Ostrovsky equation

Lett Math Phys 107 (2017), 1293-1314

Abstract:
We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all smooth periodic travelling waves independently on the nonlinearity power. The argument is based on the energy convexity and does not use coordinate transformations of the reduced Ostrovsky equations to the semi-linear equations of the Klein-Gordon type.

Keywords:
Reduced Ostrovsky equation; periodic waves; spectral stability; negative index theory;